Based on the same argument in [1]}, Eq. (REF ) represents a finite-basis model for random smooth functions whose covariance converges to some fixed form in the limit of large \(n\) . If the features in \(\Omega \)  are sampled from a distribution and remain fixed, then one can infer the weight parameters \({\bf w}\)  given the data (or hyperdata in [2]}) \({\bf Z,u}\) , the prior distribution \(p({\bf w})=\mathcal {N}(0,\sigma ^2I_{2n})\) , and observation noise variance \(\sigma _s^2\) . The notation means \({\bf Z}={\left({\begin{matrix}{\bf z}_1,&\cdots ,&{\bf z}_M\end{matrix}}\right)}\in \mathbb {R}^{D\times M}\)  and \({\bf u}={\left({\begin{matrix}u_1,&\cdots ,&u_M \end{matrix}}\right)}^T\in \mathbb {R}^{M\times 1}\) . Following the linear Bayesian learning [3]}, the posterior reads
\(p({\bf w}|{\bf Z,u})=\mathcal {N}({\bf w}|{\bar{\bf w}},A^{-1})\:,\) 
